You will receive a piece of the Pirate set after completing Isle of Lost Skulls.
The item you receive depends on your quest rating at the end of the quest.
C rank: Cuffs / Belt
B rank: Belt / Shirt
A rank: Shirt / Hat
S rank: Any piece from the black set
As with any quest, once you have obtained every piece of the black set, you will receive a piece of the lower ranks you haven't gotten yet.
All cosmetic pieces except S rank items can be bought with gold you earn during the quest, in the lobby Gift Shop.